CLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

Purpose:

CLATDF computes the contribution to the reciprocal Dif-estimate
by solving for x in Z * x = b, where b is chosen such that the norm
of x is as large as possible. It is assumed that LU decomposition
of Z has been computed by CGETC2. On entry RHS = f holds the
contribution from earlier solved sub-systems, and on return RHS = x.
The factorization of Z returned by CGETC2 has the form
Z = P * L * U * Q, where P and Q are permutation matrices. L is lower
triangular with unit diagonal elements and U is upper triangular.

Parameters:

IJOB

IJOB is INTEGER
IJOB = 2: First compute an approximative null-vector e
of Z using CGECON, e is normalized and solve for
Zx = +-e - f with the sign giving the greater value of
2-norm(x). About 5 times as expensive as Default.
IJOB .ne. 2: Local look ahead strategy where
all entries of the r.h.s. b is choosen as either +1 or
-1. Default.

LDZ is INTEGER
The leading dimension of the array Z. LDA >= max(1, N).

RHS

RHS is REAL array, dimension (N).
On entry, RHS contains contributions from other subsystems.
On exit, RHS contains the solution of the subsystem with
entries according to the value of IJOB (see above).

RDSUM

RDSUM is REAL
On entry, the sum of squares of computed contributions to
the Dif-estimate under computation by CTGSYL, where the
scaling factor RDSCAL (see below) has been factored out.
On exit, the corresponding sum of squares updated with the
contributions from the current sub-system.
If TRANS = 'T' RDSUM is not touched.
NOTE: RDSUM only makes sense when CTGSY2 is called by CTGSYL.

RDSCAL

RDSCAL is REAL
On entry, scaling factor used to prevent overflow in RDSUM.
On exit, RDSCAL is updated w.r.t. the current contributions
in RDSUM.
If TRANS = 'T', RDSCAL is not touched.
NOTE: RDSCAL only makes sense when CTGSY2 is called by
CTGSYL.

IPIV

IPIV is INTEGER array, dimension (N).
The pivot indices; for 1 <= i <= N, row i of the
matrix has been interchanged with row IPIV(i).

JPIV

JPIV is INTEGER array, dimension (N).
The pivot indices; for 1 <= j <= N, column j of the
matrix has been interchanged with column JPIV(j).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Further Details:

This routine is a further developed implementation of algorithm BSOLVE in [1] using complete pivoting in the LU factorization.